Simple Interest
Math MCQs

Question :    Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

Correct Answer  $6726

Solution & Explanation

Solution

Given,

Principal (P) = $5700

Rate of Simple Interest (SI) = 2%

Time (t) = 9 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% per annum.

Method (1) Using Formula

Calculation of Simple Interest

Formula to Calculate Simple Interest

Simple Interest (SI) = Principal × Rate × Time

Thus, Simple Interest (SI) = $5700 × 2% × 9

= $5700 ײ/₁₀₀ × 9

= ^{5700 × 2 × 9}/₁₀₀

= ^{11400 × 9}/₁₀₀

= ¹⁰²⁶⁰⁰/₁₀₀

= $1026

Thus, Simple Interest = $1026

Calculation of Amount

The total money paid to the lender by a borrower is called the Amount.

In other words, sum of priciple and interest is called the Amount.

Formula to Calculate the Amount

Amount = Principal + Interest

Thus, Amount = $5700 + $1026

= $6726

Thus, Amount to be paid = $6726 Answer

Method (2)

Calculation of Amount when Principal, Rate of Simple Interest and Time are given

Calculation of Amount directly using Principal, SI, and Time

Formula to calculate the Amount

Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)

⇒ A = P + PRT

Here in the question, P = $5700

Rate of Simple Interest (SI) or (R) = 2%

And, Time (t) = 9 years

Thus, Amount (A)

= $5700 + ($5700 × 2% × 9)

= $5700 + ($5700 ײ/₁₀₀ × 9)

= $5700 + (^{5700 × 2 × 9}/₁₀₀)

= $5700 + (^{11400 × 9}/₁₀₀)

= $5700 + (¹⁰²⁶⁰⁰/₁₀₀)

= $5700 + $1026 = $6726

Thus, Amount (A) to be paid = $6726 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 2%

This, means, $2 per $100 per year

∵ For $100, the simple interest for 1 year = $2

∴ For $1, the simple interest for 1 year = ²/₁₀₀

∴ For $5700, the simple interest in 1 year

= ²/₁₀₀ × 5700

= ^{2 × 5700}/₁₀₀

= ¹¹⁴⁰⁰/₁₀₀ = $114

Thus, simple interest for 1 year = $114

Therefore, simple interest for 9 years

= Simple interest for 1 year × 9

= $114 × 9 = $1026

Thus, Simple Interest (SI) = $1026

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $5700 + $1026

= $6726

Thus, Amount to be paid = $6726 Answer

Similar Questions

(1) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?

(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.

(4) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(6) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.

(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?

(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.